Mixed Conditional-Categorical Syllogisms from Avicenna to Urmawi

A number of medieval Arabic logicians discussed inferences that combine the principles of propositional and term logic, for example: Whenever H is Z then Every J is D No D is A Whenever H is Z then Some J is not A The present paper will be devoted to discussions of the validity of mixed conditional-categorical syllogisms of this form, and purported counterexamples, from Avicenna (d. 1037) to Urmawi (d. 1283). One major problem that was discussed, related to modern discussions of the context-sensitivity of counterfactual conditionals, is that if the antecedent of the conditional premise is incompatible with the categorical premise, then there is no guarantee that the latter will combine syllogistically with the consequent of the conditional premise. Plausible formalizations of the argument reinforce the misgivings expressed by some thirteenth-century Arabic logicians.